Optimal. Leaf size=14 \[ \frac{2 \cos (x)}{\sqrt{1-\sin (x)}} \]
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Rubi [A] time = 0.0088184, antiderivative size = 14, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 10, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.1, Rules used = {2646} \[ \frac{2 \cos (x)}{\sqrt{1-\sin (x)}} \]
Antiderivative was successfully verified.
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Rule 2646
Rubi steps
\begin{align*} \int \sqrt{1-\sin (x)} \, dx &=\frac{2 \cos (x)}{\sqrt{1-\sin (x)}}\\ \end{align*}
Mathematica [B] time = 0.0111571, size = 42, normalized size = 3. \[ \frac{2 \sqrt{1-\sin (x)} \left (\sin \left (\frac{x}{2}\right )+\cos \left (\frac{x}{2}\right )\right )}{\cos \left (\frac{x}{2}\right )-\sin \left (\frac{x}{2}\right )} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.035, size = 23, normalized size = 1.6 \begin{align*} -2\,{\frac{ \left ( -1+\sin \left ( x \right ) \right ) \left ( 1+\sin \left ( x \right ) \right ) }{\cos \left ( x \right ) \sqrt{1-\sin \left ( x \right ) }}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [F] time = 0., size = 0, normalized size = 0. \begin{align*} \int \sqrt{-\sin \left (x\right ) + 1}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [B] time = 1.60813, size = 88, normalized size = 6.29 \begin{align*} \frac{2 \,{\left (\cos \left (x\right ) + \sin \left (x\right ) + 1\right )} \sqrt{-\sin \left (x\right ) + 1}}{\cos \left (x\right ) - \sin \left (x\right ) + 1} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [F] time = 0., size = 0, normalized size = 0. \begin{align*} \int \sqrt{1 - \sin{\left (x \right )}}\, dx \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [F] time = 0., size = 0, normalized size = 0. \begin{align*} \int \sqrt{-\sin \left (x\right ) + 1}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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